We report the magnetic and electronic structures of the newly synthesized inverse-trirutile compound Cr2MoO6. Despite the same crystal symmetry and similar bond-lengths and bond-angles to Cr2TeO6, Cr2MoO6 possesses a magnetic structure of the Cr2MoO6 type, different from that seen in Cr2TeO6. Ab-initio electronic structure calculations show that the sign and strength of the Cr-O-Cr exchange coupling is strongly influenced by the hybridization between Mo 4d and O 2p orbitals. This result further substantiates our recently proposed mechanism for tuning the exchange interaction between two magnetic atoms by modifying the electronic states of the non-magnetic atoms in the exchange path through orbital hybridization. This approach is fundamentally different from the conventional methods of controlling the exchange interaction by either carrier injection or through structural distortions.